com.numericalmethod.suanshu.matrix.doubles

Class AreMatrices

java.lang.Object

com.numericalmethod.suanshu.matrix.doubles.AreMatrices

public class AreMatrices
extends java.lang.Object

These are the boolean operators that take two or more matrices or vectors and compare their properties.

Method Summary

Modifier and Type	Method and Description
static boolean	equal(Matrix A1, Matrix A2, double epsilon) Check the equality of two matrices up to a precision.
static boolean	equal(Vector v1, Vector v2, double epsilon) Check if two vectors are equal, i.e., v1 - v2 is a zero vector, up to a precision.
static boolean	orthogonal(Vector[] v, double epsilon) Check if a set of vectors are orthogonal, i.e., for any v1, v2 in v, v1 ∙ v2 == 0.
static boolean	orthogonal(Vector v1, Vector v2, double epsilon) Check if two vectors are orthogonal, i.e., v1 ∙ v2 == 0.
static boolean	orthogonormal(Vector[] v, double epsilon) Check if a set of vectors are orthogonormal.
static boolean	orthogonormal(Vector v1, Vector v2, double epsilon) Check if two vectors are orthogonormal.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

equal

public static boolean equal(Matrix A1,
                            Matrix A2,
                            double epsilon)

Check the equality of two matrices up to a precision. Two matrices are equal if

1. the dimensions are the same;
2. all entries are equal

Parameters:

A1 - a matrix

A2 - a matrix

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Returns:

true if all entries are equal, entry by entry

equal

public static boolean equal(Vector v1,
                            Vector v2,
                            double epsilon)

Check if two vectors are equal, i.e., v1 - v2 is a zero vector, up to a precision.

Parameters:

v1 - a vector

v2 - a vector

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Returns:

true if all entries are equal, entry by entry

orthogonal

public static boolean orthogonal(Vector v1,
                                 Vector v2,
                                 double epsilon)

Check if two vectors are orthogonal, i.e., v1 ∙ v2 == 0.

Parameters:

v1 - a vector

v2 - a vector

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Returns:

true the two vectors are orthogonal

orthogonal

public static boolean orthogonal(Vector[] v,
                                 double epsilon)

Check if a set of vectors are orthogonal, i.e., for any v1, v2 in v, v1 ∙ v2 == 0.

Parameters:

v - a set of vectors

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Returns:

true if any two vectors are orthogonal

orthogonormal

public static boolean orthogonormal(Vector v1,
                                    Vector v2,
                                    double epsilon)

Check if two vectors are orthogonormal. Two vectors are orthogonormal if

1. {v1, v2} are orthogonal;
2. |v1| = |v2| = 1.

Parameters:

v1 - a vector

v2 - a vector

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Returns:

true if the two vectors are orthogonormal

orthogonormal

public static boolean orthogonormal(Vector[] v,
                                    double epsilon)

Check if a set of vectors are orthogonormal.

Parameters:

v - a set of vectors

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Returns:

true if any two vectors are orthogonormal